Up and down. Initial prices are based on a demand forecast. Actual demand can be either side of that. If it's lower than expected, prices go down. If it's higher, they go up. Demand is tracked, and fares are adjusted, daily.

Fares rise near the departure date as lower fare classes sell out or become unavailable because their rules require a minimum advance booking. This lets airlines take advantage of the fact that people who book late must often make the trip at any cost, whereas for those who have more lead time it is typically more of a choice.

Bottom line: you'll see fares go up in general, especially within a month or so of departure. Day-to-day fluctuations can be in either direction.

Also, economic conditions and a wide range of external events can affect demand and therefore prices.

There are sites that claim to be able to forecast prices based on historical trends, but they have had limited success. The best-known, farecast, now redirects to Microsoft's new Bing search engine.